The planets around our sun mostly share an axis, because of how the solar system formed from a cloud of debris. So at least locally it’s a flat-ish plane. As we move farther out more distant objects no longer follow this plane as they have not been influenced strongly enough by the gravity of the other bodies in the plane.
But the next solar system over will have its own, different plane. All of the solar systems in the milky way likewise orbit on roughly the same plane.
So there is no universal plane, but things in space do tend to take on planar shapes.
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